Optimality conditions for partial information stochastic control problems driven by Lévy processes

In this paper, we consider a partial information stochastic control problem where the system is governed by a nonlinear stochastic differential equation driven by Teugels martingales associated with some Lévy process and an independent Brownian motion. We prove optimality necessary conditions in the form of a maximum principle. These conditions turn out to be sufficient under some convexity assumptions. To illustrate the general results, an example is solved.